STAT331 Final Project Report

Introduction

For our project, we want to explore the relationship between murder rate and happiness score in each country per year. We hypothesize that there will be a negative correlation between the two meaning that the higher the murder rates, the lower happiness scores. This could potentially indicate that safety and security are significant factors in overall happiness.

We obtained our data from Gapminder (n.d.).

population: contains total population counts for each country per year.
murder: contains total number of estimated deaths from interpersonal violence for each country per year.
happiness: contains happiness score (converted to 0 to 100 scale to be in terms of percentage) for each country per year.

Data Cleaning

In order to find the relationship between murder rates and happiness score for each country per year, we need to merge the total murders data set and population data set. That way, we can get the murder rate per 100K people.

Note

We first have to convert all the values into numbers (i.e. fix cases such as 1.1k to be 1100).

Code

convert_value <- function(val) {
  val <- as.character(val)
  
  multiplier <- case_when(
    str_detect(val, "k") ~ 1e3,
    str_detect(val, "M") ~ 1e6,
    str_detect(val, "B") ~ 1e9,
    TRUE ~ 1
  )
  
  numeric_value <- as.numeric(str_remove_all(val, "[kMB]"))
  
  return(numeric_value * multiplier)
}

murder_clean <- murder |>
  select(country, `2005`:`2019`) |> 
  pivot_longer(cols = `2005`:`2019`,
               names_to = "year",
               values_to = "murder_count") |> 
  mutate(across(murder_count, ~convert_value(.)))

murder_clean

population_clean <- population |>
  select(country, `2005`:`2019`) |>
  pivot_longer(cols = `2005`:`2019`,
               names_to = "year",
               values_to = "population") |>
  mutate(across(population, ~convert_value(.)))

population_clean

After cleaning the total murders and population data set, we can proceed to merging them to get a data set of the murder rate per 100k people for each country and year. We cna then use pivot longer to transform the happiness score data set and merge it with the murder rate per 100k data set to get our final data set.

Code

murder_pop_merged <- murder_clean |>
  inner_join(population_clean, by = c("country", "year"))

murder_rate_clean <- murder_pop_merged |>
  mutate(murder_rate_per_100k = (murder_count / population) * 100000)

happiness_clean <- happiness |>
  select(country, `2005`:`2019`) |>
  pivot_longer(cols = `2005`:`2019`,
               names_to = "year",
               values_to = "happiness_score") |>
   drop_na(happiness_score)

happiness_merged <- murder_rate_clean |>
  inner_join(happiness_clean, by = c("country", "year"))

happiness_merged |>
  head() |>
  knitr::kable(digits = 4) 

country	year	murder_count	population	murder_rate_per_100k	happiness_score
Afghanistan	2008	3780	26400000	14.3182	37.2
Afghanistan	2009	3870	27400000	14.1241	44.0
Afghanistan	2010	4130	28200000	14.6454	47.6
Afghanistan	2011	4170	29200000	14.2808	38.3
Afghanistan	2012	4240	30500000	13.9016	37.8
Afghanistan	2013	4380	31500000	13.9048	35.7

Final Dataset

The final data set contains 1,820 rows and 6 columns.

The columns are country, year, murder_count, population, murder_rate_per_100k, and happiness_score.

It provides a comprehensive overview of the murder rates and happiness scores across various countries and years. Each entry in the data set corresponds to a unique combination of a country and a year (ranging from 2005 to 2019).

Data Visualizations

Plot 1

Code

murder_happiness_summary <- murder_happiness |>
  group_by(country, year) |>
  summarise(avg_murder_rate = mean(murder_rate_per_100k),
            avg_happiness_score = mean(happiness_score)) |>
  ungroup()

animated_plot <- ggplot(murder_happiness_summary,
                        aes(x = avg_murder_rate,
                            y = avg_happiness_score,
                            color = as.factor(year))
                        ) +
  geom_point() +
  geom_smooth(method = "lm", color = "black") +
  labs(title = "Relationship Between Murder Rate and Happiness Score (2005-2019)",
       subtitle = "Average Happiness Score",
       x = "Average Murder Rate (per 100k)",
       y = "",
       color = "Year") +
  transition_time(year) +
  enter_fade() +
  exit_fade()

animate(animated_plot, renderer = gifski_renderer())

Plot 2

Code

country_murder_happiness <- murder_happiness |>
  group_by(country) |>
  summarise(avg_murder_rate = mean(murder_rate_per_100k),
            avg_happiness_score = mean(happiness_score))

country_murder_happiness |>
  ggplot(aes(x = avg_murder_rate, 
             y = avg_happiness_score)
         ) +
    geom_point(color = "steelblue") +
    geom_smooth(method = "lm", color = "black") +
    labs(title = "Relationship Between Murder Rate and Happiness Score",
         subtitle = "Average Happiness Score",
         x = "Average Murder Rate (per 100k)", 
         y = "") +
    theme_minimal()

Linear Regression

x (explanatory): average murder rate per 100K people
y (response): average happiness score

Code

linear_model <- lm(avg_happiness_score~avg_murder_rate, country_murder_happiness)
summary(linear_model)

Predicted Happiness Score = 54.37738 - 0.05908 x Average Murder Rate

According to the linear regression model, when the murder rate is zero, the predicted happiness score is estimated to be 54.38. Additionally, the analysis suggests that for each additional murder per 100,000 people, the predicted happiness score decreases by approximately 0.0591 points.

Model Fit

Code

var_response <- var(country_murder_happiness$avg_happiness_score)
var_fitted <- var(linear_model$fitted.values)
var_resid <- var(linear_model$residuals)
explained_variation <- var_fitted/var_response

table_data <- data.frame(
  Variable = c("Response Variable Variance", "Fitted Values Variance", "Residuals Variance", "Explained Variation"),
  Value = c(var_response, var_fitted, var_resid, explained_variation)
)

table_data |>
  knitr::kable(digits = 4) 

Variable	Value
Response Variable Variance	114.7320
Fitted Values Variance	0.3622
Residuals Variance	114.3697
Explained Variation	0.0032

The explained variation is 0.00315, which is almost 0. This means that murder rate explains almost none of the variability in happiness. Almost all of the variability in happiness is unaccounted for.

References

n.d. https://www.gapminder.org/data/.